On unitary representability of topological groups
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Títol
On unitary representability of topological groupsAutoria
Data de publicació
2009Editor
Springer VerlagISSN
0025-5874Cita bibliogràfica
GALINDO, Jorge. On unitary representability of topological groups. Mathematische Zeitschrift, 2009, vol. 263, no 1, p. 211.Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
https://link.springer.com/article/10.1007/s00209-008-0461-zVersió
info:eu-repo/semantics/submittedVersionParaules clau / Matèries
Resum
We prove that the additive group (E*, τ k (E)) of an -Banach space E, with the topology τ k (E) of uniform convergence on compact subsets of E, is topologically isomorphic to a subgroup of the unitary group of some ... [+]
We prove that the additive group (E*, τ k (E)) of an -Banach space E, with the topology τ k (E) of uniform convergence on compact subsets of E, is topologically isomorphic to a subgroup of the unitary group of some Hilbert space (is unitarily representable). This is the same as proving that the topological group (E*, τ k (E)) is uniformly homeomorphic to a subset of 2 for some κ. As an immediate consequence, preduals of commutative von Neumann algebras or duals of commutative C*-algebras are unitarily representable in the topology of uniform convergence on compact subsets. The unitary representability of free locally convex spaces (and thus of free Abelian topological groups) on compact spaces, follows as well. The above facts cannot be extended to noncommutative von Neumann algebras or general Schwartz spaces [-]
Publicat a
Mathematische Zeitschrift, 2009, vol. 263, no 1Drets d'accés
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